Solve for $x$ and $y$ using elimination. ${-3x+y = -9}$ ${-5x-y = -31}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-8x = -40$ $\dfrac{-8x}{{-8}} = \dfrac{-40}{{-8}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-3x+y = -9}\thinspace$ to find $y$ ${-3}{(5)}{ + y = -9}$ $-15+y = -9$ $-15{+15} + y = -9{+15}$ ${y = 6}$ You can also plug ${x = 5}$ into $\thinspace {-5x-y = -31}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ - y = -31}$ ${y = 6}$